Please use this identifier to cite or link to this item: http://hdl.handle.net/2289/4362

 Title: The diffeomorphism constraint operator in loop quantum gravity Authors: Laddha, AlokVaradarajan, Madhavan Issue Date: Oct-2011 Publisher: IOP Publishing Ltd. Citation: Classical and Quantum Gravity, 2011, Vol.28, p195010 Abstract: We construct the smeared diffeomorphism constraint operator at finite triangulation from the basic holonomy- flux operators of Loop Quantum Gravity, evaluate its continuum limit on the Lewandowski- Marolf habitat and show that the action of the continuum operator provides an anomaly free representation of the Lie algebra of diffeomorphisms of the 3- manifold. Key features of our analysis include: (i) finite triangulation approximants to the curvature, $F_{ab}^i$ of the Ashtekar- Barbero connection which involve not only small loop holonomies but also small surface fluxes as well as an explicit dependence on the edge labels of the spin network being acted on (ii) the dependence of the small loop underlying the holonomy on both the direction and magnitude of the shift vector field (iii) continuum constraint operators which do {\em not} have finite action on the kinematic Hilbert space, thus implementing a key lesson from recent studies of parameterised field theory by the authors. Features (i) and (ii) provide the first hints in LQG of a conceptual similarity with the so called "mu- bar" scheme of Loop Quantum Cosmology. We expect our work to be of use in the construction of an anomaly free quantum dynamics for LQG. Description: Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations) Also appairs in Journal of Physics : Conference Series, 2012, Vol.360, p012009 URI: http://hdl.handle.net/2289/4362 ISSN: 1361-6382 (Online)0264-9381 Alternative Location: http://arxiv.org/abs/1105.0636http://dx.doi.org/10.1088/0264-9381/28/19/195010http://adsabs.harvard.edu/abs/2011CQGra..28s5010L Copyright: 2011 IOP Publishing Ltd. Appears in Collections: Research Papers (TP)

Files in This Item:

File Description SizeFormat
2011_Class.Quantum Grav. V28_p195010.pdfRestricted Access383.15 kBAdobe PDFView/Open

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.